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Iterative Interstream Interference Cancellation for

MIMO HSPA+ SystemHyougyoul Yu, Byonghyo Shim, Tae Won Oh

School of Information and Communication, Korea University

Anam-dong, Sungbuk-gu, Seoul, Korea, 136-713Email: {hy lyu, bshim, taewon}@korea.ac.kr

AbstractIn this paper, we propose an iterative interstreaminterference cancellation technique for system with frequencyselective multiple input multiple output (MIMO) channel. Ourmethod is inspired by the fact that the cancellation of theinterstream interference can be regarded as a reduction in themagnitude of the interfering channel. We show that, as iterationgoes on, the channel experienced by the equalizer gets close tothe single input multiple output (SIMO) channel and, therefore,the proposed SIMO-like equalizer achieves improved equalization

performance in terms of normalized mean square error. Fromsimulations on downlink communications of22 MIMO systemsin HSPA UMTS standard, we show that the proposed methodprovides substantial performance gain over the conventionalreceiver algorithms.

I. INTRODUCTION

Recently, increasing demand for high quality data services

is fueling the deployment of high speed packet access (HSPA)

standard in UMTS mobile communication systems. In the

recent standard of HSPA referred to as HSPA+ [1], 2 2

multiple-input-multiple-output (MIMO) system [2] has beenintroduced to improve the average user throughput and the

peak data rates. For achieving the target data rate (42Mbps)

in frequency selective fading channel, an effective MIMO

receiver technique that can effectively deal with intersymbol

interference (ISI) and interstream interference is crucial. Tradi-

tionally, linear minimum mean square error (LMMSE) equal-

izer and its variants have long been employed, and these are

still popularly being used owing to the benefit on complexity

and implementation simplicity. However, because of the corre-

lation between channels each stream is experiencing (e.g., rank

loss due to small antenna spacing and/or the presence of strong

line of sight component), in many situations, MIMO equalizer

cannot properly handle the interstream interference resultingin substantial performance loss. Hence, an improved receiver

algorithm that handles both ISI and interstream interferences

is of great importance to meet the user demand and quality of

service (QoS) of the HSPA+ based UMTS system.

Previous studies include iterative interference cancelation

techniques and equalization [3][7]. The main focus of this

approach is per code channel cancellation/suppression, either

in serial [3], [5] or parallel manner [6], to reduce inter-user

interference and improve signal-to-interference-and-noise ratio

(SINR). While the key ingredient of these approaches lie on

the minimum mean square error (MMSE) based equalization

MIMO

EQTx

SIMO

EQTx

SIMO

EQTx

OP OP

Fig. 1. The illustration of (a) conventional MIMO equalizer and (b) proposedmethod.

such as the MMSE successive interference cancellation (SIC)

[3], recent focus has moved on to a posteriori probability

(APP) detection via iterative detection and decoding (IDD). In

the IDD scheme, the fast search algorithm so-called list sphere

decoding (LSD) [8] is employed to perform efficient detection

of the APP. The LSD algorithm has several variants including

K-best detector [9] and LISt-Sequential (LISS) detector [5](see, e.g., [7], for detailed discussion). Although the IDD

is a promising option for systems with a narrowband flat-fading channel model such as the MIMO-OFDM systems, they

may not be a good choice for MIMO systems with frequency

selective channel response since the dimension of the channel

matrix (roughly in the order of 10) is in general much largerthan that of the MIMO-OFDM system (mostly 2 2 and4 4) and also the dimension is not fixed because of channelvariations.

The aim of this paper is to improve the performance of

the CDMA systems with frequency selective MIMO channels

using a cost effective interstream interference cancellation.

Unlike the MMSE-SIC or MIMO-LMMSE equalizer, the

proposed method gradually converts MIMO channel into two

independent single-input-multiple-output (SIMO) channels byperforming per stream interference cancellation iteratively (see

Fig. 1). Since the SIMO channel equalizer is more robust

to the channel correlation and also provides better MSE

than the MIMO channel equalizer, the proposed equalizer

outperforms the standard MIMO equalizer in terms of mean

square error (MSE). In fact, using the simulations on downlink

communication of UMTS HSPA+ system employing 2 2MIMO transmission, we show that the proposed method offers

substantial performance gain over the conventional approach.

The remainder of this paper is organized as follows. In

Section II, the system model of the UMTS HSPA+ system and


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2

LMMSE

equalizer 1

Channel

convolution

)(

1 lx

Soft symbol

slicing

Transmit chip

generation)(

11 lI

1y +

)( ls

LMMSE

Equalizer 2

De-spreading)(

2 lx

2y

)(

1

ly

)(

2

ly

)(

22 lI

2 x 2 MIMO

Precoding

Constellation

mapperSpreadingScrambling

Constellation

mapperSpreadingScrambling

Stream 1

Stream 2

1s

2s

1x

2x

o

De-scramblingInverse

precoding

+

+

+

)(

1

ly

)(

2

ly

PO

YX

lI

PO

XY

lI

Fig. 2. The basic structure of the proposed scheme employing 22 MIMO in HSPA system.

the analysis of LMMSE equalizer in terms of the normalized

mean square error are presented. In Section III, the proposed

interstream interference cancelled SIMO equalization scheme

is proposed. The simulation results and discussion are pre-

sented in Section IV and Section V concludes the paper.

We briefly summarize notations used in this paper. We

employ uppercase and lowercase boldface letter for matrix

and vector, respectively. Notations (),()H,()T, and ()1

are used to denote the conjugate, Hermitian, transpose, and

matrix inverse operations, respectively.

I I . DOWNLINK OF UMTS HSPA SYSTEM

A. System Model and LMMSE based MIMO Equalizer

In the HSPA+ system with the MIMO transmission mode,

a precoding matrix is applied to two streams of Walsh coded

and scrambled information vectors (see Fig. 2). By denoting

the precoded transmit chip sequences as x1[n] and x2[n],respectively, the relationship between the transmit and received

sequences at each receive antenna can be expressed as

y1[n] =k

h11[k]x1[n k] +k

h12[k]x2[n k]

+ v1[n] (Antenna 1) (1)

y2[n] =k

h21[k]x1[n k] +k

h22[k]x2[n k]

+ v2[n] (Antenna 2) (2)

where yi[n] is the received signal for antenna i, hij [n] is theoverall channel impulse response (including transmit filter,

propagation channel impulse response, and receiver filter)

between the transmit antenna j and receive antenna i, andvi[n] C N(0, N0) is the complex Gaussian noise vector.

For developing the LMMSE equalizer [10] of the MIMO-

HSPA+ system, we use the following frequency domain rep-

resentation as

y1() h11()x1() + h12()x2() + v1() (3)

y2() h21()x1() + h22()x2() + v2() (4)

where yi(), xi(), hij(), and vi() are the discrete Fouriertransform (DFT) ofyi[n], xi[n], hij [n], and vi[n], respectively.Note that an approximation error caused by the DFT of the

linear convolution in (1) and (2) will be negligible if theDFT size chosen is much larger than the length of the overall

channel impulse response [11]. Using the matrix-vector form,

(3) and (4) can be simplified to

y() = H()x() + v() (5)

where y() = [y1() y2()]

H, and H() = [h1() h2()],

where h1() = [h11() h21()]

Hand h2() =

[h12() h22()]

H. Also, x() = [x1() x

2()]

H, and

v() = [v1() v2()]

H. In what follows, we drop anduse y = Hx + v for notational simplicity.

The linear MMSE estimate x ofx is [12], [13]

x = RxyR1yy (y E[y]). (6)

Using E[xxH] = SI and E[|v|2] = N0I, the crosscorrelationRxy between y and x becomes Rxy = SH

H and the auto-

correlation of y is Ryy =(SHHH + N0I

). These together

with the fact that E[y] = 0, we have

x = SHH(SHHH + N0I

)1y

=S

N0HH

S

N0HHH + I

1y. (7)

By taking the inverse FFT of x, we can obtain the equalized

chip sequence x[n].


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B. NMSE Analysis of HSPA MIMO Equalizer

In this subsection, we investigate the asymptotic behavior

of the LMMSE based MIMO equalizer for HSPA+ system for

motivating our approach of interstream interference cancelled

equalizer in Section III. Towards the end, we consider the

normalized covariance Cnorm(x, x) =1SE[|x x|2] of the

LMMSE estimate in (7). It is well-known that E[|x x|2] =

(R1xx + H

H

R1vvH)

1

[12] and hence

Cnorm(x, x) =1

S

1

SI+

1

N0HHH

1

=(I+ SNRHHH

)1(8)

where Rxx = SI, Rvv = N0I, and SNR =SN0

. Furthermore,

if h1 and h2 denote the first and second column vectors of

H, respectively, then we have

Cnorm(x, x) = (I+ SNRHHH)1

=

1 + SNRh12 SNRhH1 h2

SNRhH2 h1 1 + SNRh22

1.

(9)

Note that the (1, 1)-th element of Cnorm(x, x), correspondingto the normalized mean square error (NMSE) of the first

stream, is expressed as

NMSE(x1, x1)

=1 + SNRh22

(1 + SNRh12)(1 + SNRh22) SNR2|hH1 h2|

2

=1

1 + SNRh12 SNR2|hH

1h2|2

(1+SNRh22)

=1

SNR

h12 |hH1h2|2

h22+1

SNR + 1SNR . (10)

Similarly, one can show that

NMSE(x2, x2) =1

SNR

h22 |hH2h1|2

h12+1

SNR

+ 1SNR

. (11)

This result reveals that the equalizer performance depends

not only on the SNR but also on the relationship between

the two channel vectors h1 and h2. Let (H,SNR) =h12

|hH1h2|

2

h22+1

SNR

+ 1SNR

, then

NMSE(x1, x1) =1

SNR(H, SNR)

. (12)

(12) provides direction for improvement. First, it is clear

from (12) that two factors determining the performance of

the LMMSE equalizer is the SNR and (H,SNR), which isapproximately a correlation between the two channel vectors.1

While it is true that the correlation between the two channel

vectors cannot be reduced directly, by canceling the second

stream interference, we can effectively reduce the power ofh2(i.e., increase (H, SNR)) and hence achieves smaller NMSE.

1In the high SNR region, (H, SNR) is approximated to h12 |hH1h2|

2

h22= h12(1 cos2) where is the angle between h1 and h2.

III. ITERATIVE INTERSTREAM INTERFERENCE

CANCELLATION

The proposed scheme employs interstream interference

cancellation to improve the equalizer performance. The key

observation in our approach is that the cancellation ofx2 canbe interpreted as the reduction in the magnitude ofh2, which

can be translated into reduction in the NMSE of x1. In the

same way, cancellation ofx1 will result in the reduction of theNMSE of x2. To achieve this goal, two separate equalizers,one for x1 estimation and the other for x2 estimation, areemployed (see Fig. 1). As shown in Fig. 2, the proposed

scheme consists of two sets of equalizer followed by inverse

precoding, channel despreader, symbol slicer, retransmission

chain, and interference canceller.

A. Interstream Interference Cancellation

The cancellation process of the proposed method is done

separately for each stream. In the input of the first equalizer

for estimating x1, the second stream is cancelled out and hence

the new observation becomesy1

= h11x1 + h12(x2 x2) + v1 (13)

y2 = h21x1 + h22(x2 x2) + v2 (14)

where x2 is the estimated stream of x2. Similarly, the newobservation for the second equalizer is

y1 = h11(x1 x1) + h12x2 + v1 (15)

y2 = h21(x1 x2) + h22x2 + v2. (16)

Since the treatment of y and y is essentially same, wefocus only on the y in the sequel. Rewriting (7), the equalizeroutput x2 can be expressed as

x2 = SNRhH2(

SNRh1hH1 + SNRh2hH2 + I

)1 y. (17)

Using the matrix inversion lemma [14], (17) becomes,

x2 =SNRhH2

1h2

1 + SNRhH2 1h2

x2 +SNRhH2

1h1

1 + SNRhH2 1h2

x1

+SNRhH2

1

1 + SNRhH2 1h2

v (18)

where = SNRh1hH1 + I. Under the assumption that

hH2 1h2 is larger than h

H2

1h1 and hH2

1v, x2 SNRhH

21h2

1+SNRhH21h2

x2 and hence (13) and (14) becomes

y1

h11x1 + h12x2 + v1 (19)y2

h21x1 + h22x2 + v2 (20)

where = 11+SNRhH

21h2

indicates the amount of attenua-

tion of the interstream interference x2 in y. The vector form

of (19) and (20) is y [h1 h2

]x + v and the NMSE

in (10) is rewritten as

NMSE(x1, x1) =1

SNR

h12 2|hH

1h2|2

2h22+1

SNR

+ 1SNR

. (21)

As shown in Fig. 3(a), when decreases, the denominatorincreases and thereby reduces NMSE(x1, x1). General form


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0 5 10 15 20

102

101

SNR (dB)

NMSE

= 0.0

= 0.1

= 0.3

= 0.5

= 0.7

= 0.9

= 1.0

(a) NMSE as a function of.

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Iteration number

SNR = 0 dB

SNR = 10 dB

SNR = 20 dB

SNR = 30 dB

(b) as a function of iteration number.

Fig. 3. NMSE and as a function of SNR and iteration number, respectively

of the observation vector when we perform an iterative inter-

stream cancellation is

y(+1) [h1 h2

]x + v (22)

where is the attenuation factor of the interstream inter-ference x2 at the -th iteration. Noting that E[

x2 x22] E[| x2|

2] = 2S and also recalling that NMSE(x2, x2) =

1SE[x2 x2

2

], we have

+1 = 1SNR

h22

2|hH2h1|2

2h12+

1

SNR

+ 1SNR

. (23)

We observe from Fig. 3(b) that decreases as the iterationnumber increases. However, it converges fast so that maximal

performance gain can be achieved with only a few iterations.

B. Nonlinear MMSE based Soft Symbol Slicing and Retrans-

mission

In order to ensure the performance improvement of the

proposed method over the MIMO equalization technique, re-

liability of the symbol decision process should be guaranteed.

Since it is well known that hard slicing often causes an errorpropagation [15], we employ the nonlinear MMSE estimation

for symbol slicing. Denoting the input of symbol slicer as

ri[n] = si[n] + i[n] (24)

where si[n] and i[n] are the symbol and noise after the equal-ization, inverse precoding, descrambling and despreading. The

output of the NL-MMSE based soft slicer is [12]

si[n] = arg maxm

E[sm | ri]

= arg maxm

msmP(ri|sm)P(sm)

mP(ri|sm)P(sm). (25)

Under the equal prior assumption on P(sm) and Gaussianmodel for i[n], (25) becomes

si[n] = argmaxm

msm exp

|ri[n]sm|2

22

m exp

|ri[n]sm|2

22

(26)

where the noise power 2 can be obtained using the pilotsignal as 2 =

12E[|ri[n] ri[n 1]|

2]. For a high SNR

condition (s2i

2 1

), the MMSE estimate approximates to the

hard decision since a single exponential term gets close to 1

while all other terms become negligible. On the contrary, as

no dominant term exists for a code channel with low SNR, one

can observe that si[n] is expressed as the sum of several termsand thus the magnitude of si[n] will be moderately small.Owing to the suppression of the unreliable symbol, the NL-

MMSE symbol slicing is in general more robust to the error

propagation than the hard decision based symbol slicing.

Finally, retransmission follows the footstep of the basesta-

tion transmission and is composed of Hadamard transform,

scrambling, precoding, and convolution with the channel im-

pulse response. The reconstructed interstream interferences

used for x1 and x2 estimation are given by

I(+1)i1 [n] = hi2[n] x

()2 [n] (27)

I(+1)i2 [n] = hi1[n] x

()1 [n] (28)

where x()1 and x

()2 are the retransmitted chip sequence at the

-th iteration (see Fig. 2).

IV. SIMULATION RESULTS AND DISCUSSION

A. Simulation Setup

In our simulation, we evaluate the performance of the

proposed method in the downlink of the HSPA+ system. The


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TABLE ICHANNEL PARAMETERS FOR SIMULATIONS

ITU pedestrian A channel

Tap 1 2 3 4 5 6Relative delay (ns) 0 110 190 410 - -

Average power (dB) 0.0 -9.7 -19.2 -22.8 - -

ITU pedestrian B channel

Tap 1 2 3 4 5 6Relative delay (ns) 0 200 800 1200 2300 3700

Average power (dB) 0.0 -0.9 -4.9 -8.0 -7.8 -23.9

simulated propagation channel is generated based on the ITU

Pedestrian A and B (Ped. A and B) model [16] (see table I).

Seven physical layer data channels (HS-PDSCH) with QPSK

modulation are used to generate a transmit datastream. As a

measure for the performance, the bit error rate (BER) of data

channels is used.

B. Simulations Results

5 10 15 20 25 30

103

102

101

SNR (dB)

BER

Rake

LMMSE MIMO equalizer

Proposed method (Iter=1)



Fig. 4. BER performance for SNR variation.

Fig. 4 shows the BER performance of conventional methods

[17] including the Rake and LMMSE MIMO equalizer as

well as the proposed method. Due to the existence of stronginterstream interference, we expect that the proposed approach

outperforms the conventional MIMO equalizer. Also, as men-

tioned in Section III.A, we expect that the gain obtained per

iteration diminishes so that most of gain is achieved at the

first and second iterations. For example, at 0.5% BER, theproposed method achieves about 2.5 dB (after first iteration)and 3 dB (after second iteration) gain when compared with

the LMMSE equalizer, while the gain after the third iteration

is almost same as that of the second iteration.

In Fig. 5, we check the performance of the LMMSE

equalizer and the proposed method for various slicing options.

5 10 15 20 25 30

103

102

101

SNR (dB)

BER

LMMSE MIMO equalizer (Hard slicing)

Proposed method (Hard slicing)

LMMSE MIMO equalizer (Linear MMSE slicing)

Proposed method (Linear MMSE slicing)

LMMSE MIMO equalizer (NLMMSE slicing)

Proposed method (NLMMSE slicing)

Fig. 5. BER performance of proposed method for various slicing options(Iter=1).

APP

generation

Channel

decoder

AL

Symbol slicing

Transmit chip

generation

bEL

1

)( ls

Fig. 6. The structure of proposed method employing channel decoder. LE ,

and LA are a priori information and extrinsic information of the decoder,respectively, and b is the decoded binary bit.

In our experiment, we test the soft slicing (nonlinear MMSE

slicing), linear MMSE slicing, and hard slicing. These results

clearly demonstrate that the performance of the proposed

approach depends strongly on the symbol estimation quality.

Specifically, when the hard slicing is employed, the proposed

approach suffers almost 1 dB loss over the conventionalMIMO equalizer because the accumulation of the estimation

error induces error propagation. In contrast, as the NL-MMSE

slicing moderates the effect of error propagation by suppress-

ing unreliable symbols, the proposed scheme with the NL-MMSE slicing outperforms that with the linear MMSE slicing

and hard slicing as well as the conventional MIMO equalizer.

Finally, we check the performance of the proposed scheme

when a channel decoder is employed. In this case, as shown

in Fig. 6, the APP generation, interleaver (deinterleaver), and

the channel decoder are additionally required between the

soft symbol slicer and transmit chip generator. As a channel

decoder, standard 3GPP half rate (r = 1/2) Turbo codewith g0(D) = 1 + D

2 + D3 and g1(D) = 1 + D + D3 is

employed [1] and the iteration number of the Turbo decoder

is set to 8. Fig. 7 shows the BER performance of the proposed


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6 6.5 7 7.5 8 8.5 9 9.5 1010

4

103

102

SNR (dB)

BER

LMMSE MIMO equalizer




Fig. 7. BER performance of the proposed method with channel decoding.

method employing channel decoding. Since the scheme with

the channel decoder generates symbols with improved error

performance, re-generated interstream interferences becomes

more accurate, and hence the effective channel gets closer to

the SIMO channel. Indeed, as shown in Fig. 7, the proposed

method brings significantly better algorithmic gain as well

as the diversity gain than the scheme without decoder. For

example, at 0.01% BER, the gain of the proposed method over

the conventional MIMO equalization is 1.5 dB after the firstiteration, and that increases to 2 and 2.3 dB after the secondand third iterations, respectively.

V. CONCLUSION

The main purpose of this work is to provide an interstream

interference cancellation strategy for CDMA system with

frequency selective MIMO channels. Motivated by the fact

that the SIMO equalizer is more robust to ill-behavior of

channel than MIMO equalizer, we employed the iterative

interstream interference cancellation and SIMO equalization

for improving the performance of MIMO-CDMA systems.

From the simulation on downlink of HSPA+ system, weobserved that the proposed method achieves substantial gain

over the conventional LMMSE MIMO equalization. Other

than the HSPA+ applications primarily considered in this

paper, the proposed method can be applied to any system

under frequency selective MIMO channels (e.g., single-carrier

frequency domain equalization [10] in LTE-uplink)

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